Average Error: 39.1 → 39.1
Time: 3.4s
Precision: binary64
\[\frac{\sqrt{x - 1}}{x + 1} - \frac{\sqrt{x + 1}}{x - 1}\]
↓
\[\frac{\sqrt{x - 1}}{x + 1} - \frac{\sqrt{x + 1}}{x - 1}\]
\frac{\sqrt{x - 1}}{x + 1} - \frac{\sqrt{x + 1}}{x - 1}
↓
\frac{\sqrt{x - 1}}{x + 1} - \frac{\sqrt{x + 1}}{x - 1}
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x - 1.0)))) / ((double) (x + 1.0)))) - ((double) (((double) sqrt(((double) (x + 1.0)))) / ((double) (x - 1.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sqrt(((double) (x - 1.0)))) / ((double) (x + 1.0)))) - ((double) (((double) sqrt(((double) (x + 1.0)))) / ((double) (x - 1.0))))));
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.1

    \[\frac{\sqrt{x - 1}}{x + 1} - \frac{\sqrt{x + 1}}{x - 1}\]

  2. Final simplification39.1

    \[\leadsto \frac{\sqrt{x - 1}}{x + 1} - \frac{\sqrt{x + 1}}{x - 1}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(- (/ (sqrt (- x 1)) (+ x 1)) (/ (sqrt (+ x 1)) (- x 1)))"
  :precision binary64
  (- (/ (sqrt (- x 1.0)) (+ x 1.0)) (/ (sqrt (+ x 1.0)) (- x 1.0))))